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A072543 Numbers whose largest decimal digit is also the initial digit. 4
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 30, 31, 32, 33, 40, 41, 42, 43, 44, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 110, 111, 200, 201 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A054055(a(n)) = A000030(a(n));
the sequence differs from A009996, A032873 and A032907: a(66)=101 is not in A009996, a(67)=110 is not in A032873 and a(65)=100 is not in A032907.
LINKS
EXAMPLE
a(10^ 1) = 9
a(10^ 2) = 411
a(10^ 3) = 6216
a(10^ 4) = 73474
a(10^ 5) = 813826
a(10^ 6) = 8512170
a(10^ 7) = 88368780
a(10^ 8) = 911960211
a(10^ 9) = 9237655227
a(10^10) = 93323313303
MAPLE
for i from 1 to 10 do A[i]:= i-1 od:
count:= 10:
for i from 1 to 9 do P[i]:= [seq([j], j=0..i)]; od:
for d from 2 to 4 do
for x from 1 to 9 do
for p in P[x] do
count:= count+1;
A[count]:= add(p[k]*10^(k-1), k=1..d-1) + x*10^(d-1);
od:
P[x]:= [seq(seq([op(v), t], v=P[x]), t=0..x)];
od
od:
seq(A[i], i=1..count); # Robert Israel, Feb 01 2015
MATHEMATICA
Select[Range[0, 250], Max[IntegerDigits[#]]==First[IntegerDigits[#]]&] (* Harvey P. Dale, Apr 28 2016 *)
PROG
(Haskell)
a072543 n = a072543_list !! (n-1)
a072543_list = [x | x <- [0..], a054055 x == a000030 x]
-- Reinhard Zumkeller, Apr 25 2012
(PARI) is(n)=n=digits(n); !#n || n[1]==vecmax(n) \\ Charles R Greathouse IV, Jan 02 2014
(PARI) a(n)={d = 0; r = 1; s = 0; i = 0; if(n == 1, 0, n-=2; while(n > sum(i=0, 9, (i+1)^d), n-=sum(i=0, 9, (i+1)^d); n++; d++); while(n >= (r+1)^d, n -= (r+1)^d; r++); s = r * 10^d; while(n, s += 10^i*(n%(r+1)); n \= (r+1); i++)); s } \\ David A. Corneth, Jan 31 2015
CROSSREFS
Cf. A072544.
Sequence in context: A247754 A084383 A032873 * A009996 A032907 A130576
KEYWORD
nonn,base,easy
AUTHOR
Reinhard Zumkeller, Aug 04 2002
EXTENSIONS
Offset corrected by Reinhard Zumkeller, Apr 25 2012
STATUS
approved

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Last modified April 20 15:59 EDT 2024. Contains 371844 sequences. (Running on oeis4.)